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An inverse problem for the fractionally damped wave equation

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arxiv 2307.16065 v1 pith:KRHMLAUS submitted 2023-07-29 math.AP

Li Li , Yang Zhang This is my paper · ORCID
classification math.AP
keywords equationproblemcoefficientfractionalinverseknowledgenonlinearwave
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We consider an inverse problem for a Westervelt type nonlinear wave equation with fractional damping. This equation arises in nonlinear acoustic imaging, and we show the forward problem is locally well-posed. We prove that the smooth coefficient of the nonlinearity can be uniquely determined, based on the knowledge of the source-to-solution map and a priori knowledge of the coefficient in an arbitrarily small subset of the domain. Our approach relies on a second order linearization as well as the unique continuation property of the spectral fractional Laplacian.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. An Inverse Obstacle Problem for the Fractional Schr\"odinger Equation

    math.AP 2026-07 accept novelty 6.0 of 10

    A countable family of scaled exterior measurements of the fractional Schrödinger obstacle problem determines the nonnegative potential throughout the domain.

  2. A Calder\'on type inverse problem for the active scalar equations with fractional dissipation

    math.AP 2024-12 reject novelty 6.0 of 10

    If two active scalar equations with fractional dissipation produce the same observations on a small open set, their nonlocal drift operators must agree on the whole exterior, according to the paper's main theorem.

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